This document is a final report for a study project on using quantum tunneling to explain olfaction in animals. It discusses theories of how smell receptors in the nose detect different odors at a molecular level. The report summarizes the process of quantum tunneling and how it applies to electron transport. It also reviews two main theories of olfaction - the lock and key model where odor molecules precisely fit receptor sites, and an alternate "swipe card" model where vibration frequencies also carry identifying information during smell detection through a process of inelastic electron tunneling. The report aims to understand these molecular mechanisms in more detail to help explain the phenomenon of smell.
1) The document discusses rotational (microwave) spectroscopy and the conditions for molecules to be microwave active. Only polar molecules with a permanent dipole moment can absorb microwave radiation.
2) It presents the expression for the moment of inertia of a diatomic rigid rotator molecule. The moment of inertia depends on the reduced mass and bond length.
3) The energy levels of a diatomic rigid rotator are quantized. The rotational energy increases with the rotational quantum number J and is proportional to the rotational constant B, which is specific to each molecule.
The document provides an introduction to nuclear chemistry, which deals with the study of atomic nuclei and nuclear reactions. It discusses the composition of nuclei, which contain protons and neutrons. The number of protons defines the element, while the total number of protons and neutrons is the mass number. The document also summarizes two nuclear models - the nuclear shell model, which proposes protons and neutrons exist in shells, and the liquid drop model, which views the nucleus as a homogeneous drop with short-range nuclear forces. Examples of nuclear reactions like alpha-induced and proton-induced reactions are also briefly described.
This document provides an overview of molecular spectroscopy and the types of molecular spectra. It discusses the different regions of the electromagnetic spectrum and the types of molecular transitions each induces. Energy level diagrams are presented to illustrate electronic, vibrational, and rotational transitions in molecules. The concept of degrees of freedom in polyatomic molecules is explained, showing how the total degrees of freedom are divided among translational, rotational, and vibrational components. Examples are given to calculate the vibrational degrees of freedom for different linear and non-linear molecules.
Smell in real noses: how the environment changes vibrationsVorname Nachname
This document discusses Benjamin Yiwen Färber's research into how the vibrational frequency of odor molecules is affected by the environment inside the nose. It begins by summarizing the biological process of smell and Turin's theory that odor discrimination is based on the vibrational frequencies of molecules. It then models odor molecules as diatomic harmonic oscillators and examines how the oscillator's frequency is altered by environmental factors like external charges and binding to olfactory receptors. The document relates the harmonic oscillator model to the quantum mechanical Morse potential model and tight binding model of diatomic molecules.
We propose a possible experimental realization of a quantum analogue
of Newton's cradle using a configuration which starts from a
Bose-Einstein condensate. The system consists of atoms with two
internal states trapped in a one dimensional tube with a longitudinal
optical lattice and maintained in a strong Tonks-Girardeau regime at
maximal filling. In each site the wave function is a superposition of
the two atomic states and a disturbance of the wave function
propagates along the chain in analogy with the propagation of
momentum in the classical Newton's cradle. The quantum travelling
signal is generally deteriorated by dispersion, which is large for a
uniform chain and is known to be zero for a suitably engineered
chain, but the latter is hardly realizable in practice. Starting from
these opposite situations we show how the coherent behaviour can be
enhanced with minimal experimental effort.
Coexistence of Superconductivity and Itinerant Ferromagnetism in Ucogeijrap
The coexistence of BCS superconductivity and itinerant ferromagnetism in uranium based intermetallic systems is analyzed using a Hubbard Hamiltonian. To obtain the superconducting transition
temperatureTC and Curie temperatureTFM , we used the Green’s function method. The order parameter of superconductivity ( ∆ ) and ferromagnetism ( m or I) are obtained in the mean field approximation. It is found that there generally exist coexistent solutions to coupled equations of the order parameter in the temperature range ( ) T TC TFM 0 < < min , . In our model, ferromagnetism is itinerant and therefore carried by the conduction electrons. This arises from a splitting of the spin-up and spin- down band. A consequence is that the ferromagnetism and superconductivity is carried by same electrons. Expressions for specific heat, energy spectra and density of states are derived. The specific heat has linear temperature dependence as opposed to that of the exponential decrease in the BCS theory. The density of states for a finite magnetic order parameter increases as opposed to that of a ferromagnetic metal. The theory is
applied to explain the observations in uranium based intermetallic compoundUCoGe . The agreement between theory and experiments is quite encouraging.
1. Quark potential and classical spring potential are analogous in some ways. Quark-quark interactions resemble a harmonic oscillator or stretched spring, with greater forces required to separate quarks as distance increases due to confinement.
2. Meson potentials can be modeled as a combination of coulomb, linear confinement, and oscillator terms similar to spring potential equations. The quark potential is directly proportional to quark separation distance, analogous to spring potential and displacement.
3. Both quark and spring potentials possess kinetic energy - potential energy in quarks and springs can be transformed to kinetic energy through gluons or release after stretching, respectively. Differences include deformation limits and effects of strong fields on quarks.
1) The document discusses rotational (microwave) spectroscopy and the conditions for molecules to be microwave active. Only polar molecules with a permanent dipole moment can absorb microwave radiation.
2) It presents the expression for the moment of inertia of a diatomic rigid rotator molecule. The moment of inertia depends on the reduced mass and bond length.
3) The energy levels of a diatomic rigid rotator are quantized. The rotational energy increases with the rotational quantum number J and is proportional to the rotational constant B, which is specific to each molecule.
The document provides an introduction to nuclear chemistry, which deals with the study of atomic nuclei and nuclear reactions. It discusses the composition of nuclei, which contain protons and neutrons. The number of protons defines the element, while the total number of protons and neutrons is the mass number. The document also summarizes two nuclear models - the nuclear shell model, which proposes protons and neutrons exist in shells, and the liquid drop model, which views the nucleus as a homogeneous drop with short-range nuclear forces. Examples of nuclear reactions like alpha-induced and proton-induced reactions are also briefly described.
This document provides an overview of molecular spectroscopy and the types of molecular spectra. It discusses the different regions of the electromagnetic spectrum and the types of molecular transitions each induces. Energy level diagrams are presented to illustrate electronic, vibrational, and rotational transitions in molecules. The concept of degrees of freedom in polyatomic molecules is explained, showing how the total degrees of freedom are divided among translational, rotational, and vibrational components. Examples are given to calculate the vibrational degrees of freedom for different linear and non-linear molecules.
Smell in real noses: how the environment changes vibrationsVorname Nachname
This document discusses Benjamin Yiwen Färber's research into how the vibrational frequency of odor molecules is affected by the environment inside the nose. It begins by summarizing the biological process of smell and Turin's theory that odor discrimination is based on the vibrational frequencies of molecules. It then models odor molecules as diatomic harmonic oscillators and examines how the oscillator's frequency is altered by environmental factors like external charges and binding to olfactory receptors. The document relates the harmonic oscillator model to the quantum mechanical Morse potential model and tight binding model of diatomic molecules.
We propose a possible experimental realization of a quantum analogue
of Newton's cradle using a configuration which starts from a
Bose-Einstein condensate. The system consists of atoms with two
internal states trapped in a one dimensional tube with a longitudinal
optical lattice and maintained in a strong Tonks-Girardeau regime at
maximal filling. In each site the wave function is a superposition of
the two atomic states and a disturbance of the wave function
propagates along the chain in analogy with the propagation of
momentum in the classical Newton's cradle. The quantum travelling
signal is generally deteriorated by dispersion, which is large for a
uniform chain and is known to be zero for a suitably engineered
chain, but the latter is hardly realizable in practice. Starting from
these opposite situations we show how the coherent behaviour can be
enhanced with minimal experimental effort.
Coexistence of Superconductivity and Itinerant Ferromagnetism in Ucogeijrap
The coexistence of BCS superconductivity and itinerant ferromagnetism in uranium based intermetallic systems is analyzed using a Hubbard Hamiltonian. To obtain the superconducting transition
temperatureTC and Curie temperatureTFM , we used the Green’s function method. The order parameter of superconductivity ( ∆ ) and ferromagnetism ( m or I) are obtained in the mean field approximation. It is found that there generally exist coexistent solutions to coupled equations of the order parameter in the temperature range ( ) T TC TFM 0 < < min , . In our model, ferromagnetism is itinerant and therefore carried by the conduction electrons. This arises from a splitting of the spin-up and spin- down band. A consequence is that the ferromagnetism and superconductivity is carried by same electrons. Expressions for specific heat, energy spectra and density of states are derived. The specific heat has linear temperature dependence as opposed to that of the exponential decrease in the BCS theory. The density of states for a finite magnetic order parameter increases as opposed to that of a ferromagnetic metal. The theory is
applied to explain the observations in uranium based intermetallic compoundUCoGe . The agreement between theory and experiments is quite encouraging.
1. Quark potential and classical spring potential are analogous in some ways. Quark-quark interactions resemble a harmonic oscillator or stretched spring, with greater forces required to separate quarks as distance increases due to confinement.
2. Meson potentials can be modeled as a combination of coulomb, linear confinement, and oscillator terms similar to spring potential equations. The quark potential is directly proportional to quark separation distance, analogous to spring potential and displacement.
3. Both quark and spring potentials possess kinetic energy - potential energy in quarks and springs can be transformed to kinetic energy through gluons or release after stretching, respectively. Differences include deformation limits and effects of strong fields on quarks.
This document discusses the relationship between vibrational frequency and the force constant of a covalent bond. It states that for a diatomic molecule acting as a simple harmonic oscillator, the restoring force is proportional to displacement, as described by Hooke's Law. It then provides the equation relating vibrational frequency, force constant, and reduced mass. Several examples are given of calculating force constants from given vibrational frequencies and reduced masses. The document also notes that a higher force constant corresponds to a stronger covalent bond.
Quantum mechanics is the science of the very small that explains the behavior of matter and energy at the atomic and subatomic level. Some key aspects of quantum mechanics include wave-particle duality, Heisenberg's uncertainty principle, Schrodinger's wave equation, quantum superposition, quantum entanglement, and more. Many experiments such as the double slit experiment provide evidence of these quantum effects.
D:\Edit\Super\For Submission 20100306\12622 0 Merged 1267687011Qiang LI
This document discusses a proposed mechanism for electron pairing and superconductivity in ionic crystals. It analyzes a one-dimensional ion lattice chain model and establishes a mechanism for electron pairing driven by lattice vibration modes. The analysis is extended to 3D ionic crystals, focusing on donor-acceptor systems. Electron pairing occurs between energy levels matched to the maximum vibration frequency ωM. Introducing an acceptor band can stabilize electron pairs across the acceptor and full bands, with a binding energy estimated to be at least hωM/(4π).
(v3) Phonon as carrier of electromagnetic interaction between vibrating latti...Qiang LI
With emphasis on time-dependency of electron-lattice system, we suggest the fallacy of presumed quantization in the context of electron-lattice system and propose the definition of phonons as carriers of electromagnetic interaction between electrons and vibrating lattice. We have investigated behaviors of electron-lattice system relating to “measured” energy, identified non-stationary steady state of electrons engaging in “electron pairing by virtual stimulated transitions”, recognized some origins of binding energy of electron pairs in crystals, and explained the state of electrons under pairing. Moreover, we have recognized the behavior and role of threshold phonon, which exists in electron pairing and is released by the electron from excited state, and have recognized the redundancy of the threshold phonon when the electrons under pairing have entered non-stationary steady state. We have also studied the effect of the stability of lattice wave on the evolution of the function of transition probability and on the stability of phonon-mediated electron pairs, the competition among multiple pairings associated with one same ground state, and determination of presence/absence of superconductivity by such competition.
This document summarizes elementary particles in physics. It describes how particles are classified into leptons and hadrons. Leptons include electrons, muons, taus and their neutrinos. Hadrons include baryons like protons and neutrons, and mesons. Interactions are also classified, including the electromagnetic, weak, and strong interactions. The electromagnetic interaction between charged leptons and photons is described based on local gauge invariance, resulting in a theory of quantum electrodynamics that agrees well with experiments.
1. The document discusses the derivation of de Broglie's equation relating the wavelength of matter waves to the momentum of particles. It then derives different forms of de Broglie's wavelength equation using kinetic energy and potential energy.
2. It lists properties of matter waves including that lighter particles have greater wavelengths. It derives the Schrodinger time-independent and time-dependent wave equations.
3. It applies the time-independent equation to a particle in an infinite square well, finding the wavefunctions and energy levels based on boundary conditions and normalization.
Dielectric Dilemma 1901.10805 v2 feb 4 2019Bob Eisenberg
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the epolarization of the vacuumf ..0 .......... Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws reliably describe circuits that switch in nanoseconds.
This document analyzes the phenomenon of electrostatic attraction between particles from an energy perspective. It proposes that the potential energy between charges is infinite, and justifies this through several analyses. It uses concepts from magnetism, relativity, and Maxwell's equations to show that the magnetic force originating from electron spin is the source of the electrostatic force between charges. This explains the continuous attraction of particles despite vibration and over time. Previous works only considered the energy needed to separate particles, but not the infinite energy holding them together.
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
петр карпов и сергей мухин статья магнитные вихриeconadin
This document summarizes research on the dielectric susceptibility of magnetoelectric thin films containing magnetic vortex-antivortex dipole pairs. Key points:
1) A model is proposed where magnetic vortices in the thin film possess electric charges due to magnetoelectric coupling, forming electric dipoles with antivortices.
2) Below the Berezinskii-Kosterlitz-Thouless transition temperature, vortex-antivortex pairs dominate over individual vortices due to lower energy.
3) The contribution of these magnetic vortex-antivortex dipoles to the dielectric susceptibility of the material is calculated. It is shown that the susceptibility diverges as the temperature approaches the BKT
The document summarizes a study investigating the dielectric susceptibility of magnetoelectric thin films containing magnetic vortex-antivortex pairs. The study models the magnetic subsystem using the XY model and incorporates a magnetoelectric coupling term. Magnetic vortices acquire electric charges proportional to their topological charge. Vortex-antivortex pairs form electric dipoles that contribute to the dielectric susceptibility. In the approximation of non-interacting dipole pairs, the susceptibility diverges as temperature approaches the Berezinskii-Kosterlitz-Thouless transition temperature. At low temperatures, the susceptibility takes an exponential form reflecting the thermal activation of vortex pairs.
This document discusses microwave spectroscopy and its application to determining properties of gas phase molecules. It can be summarized as follows:
1) Microwave spectroscopy utilizes photons in the microwave range to cause rotational energy level transitions in gas molecules. It is applicable to molecules with a permanent dipole moment in the gas phase.
2) The rotational energy levels of diatomic molecules can be modeled using a rigid rotor approximation. This allows derivation of an expression for rotational energy levels in terms of the rotational constant B, which depends on the molecule's moment of inertia.
3) Measurement of transition frequencies between rotational energy levels allows determination of the rotational constant B. This can then be used to calculate bond distances in diatomic molecules.
This document provides a list and overview of various subatomic and composite particles categorized by type, including:
- Elementary particles like fermions (quarks and leptons) and bosons that mediate forces
- Hypothetical particles predicted by theories like supersymmetry
- Composite particles like hadrons (baryons like protons/neutrons and mesons) and atomic/molecular structures
It describes key properties and classifications of the different particles, such as their constituents, charges, and roles in the standard model of particle physics.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
1) The document derives both the Schrodinger quantum equation and Einstein's relativistic energy-momentum relation from Maxwell's electric wave equation.
2) It does so by considering particles as oscillators and using Planck's quantum hypothesis. The electric field intensity vector is replaced by the wave function.
3) Several steps and equations are shown to first derive the Schrodinger equation, and then the electric polarization and special relativity concepts are used to derive Einstein's energy-momentum relation.
1) Maxwell's equations describe electromagnetic waves propagating through space and time. For time-varying fields, the full set of Maxwell's equations must be used.
2) By assuming time-harmonic fields with a sinusoidal time variation, Maxwell's equations can be simplified to phasor forms containing only spatial derivatives.
3) The phasor forms of Maxwell's equations can be reduced to Helmholtz wave equations for the electric and magnetic fields. Plane wave solutions representing uniform electromagnetic waves propagating in a given direction can be derived from these equations.
Lasers have several key characteristics including monochromaticity, directionality, intensity, and coherence. They work by inducing stimulated emission of photons from atoms in an excited meta-stable state, achieving population inversion. This process is triggered by stimulated emission and results in an intense, highly directional beam of coherent, monochromatic light. Common lasers include ruby, helium-neon, and semiconductor diode lasers. Lasers have numerous applications due to their unique light properties.
Experimental nonlocal and surreal Bohmian trajectories.Fausto Intilla
The document summarizes an experiment that examines nonlocal and surreal Bohmian trajectories by entangling two photons and determining the trajectory of one photon using weak measurements and postselection. The experiment aims to validate the resolution proposed by Hiley et al. that the seemingly contradictory behavior of Bohmian trajectories predicted in the presence of a Welcher Weg measurement device is due to the manifest nonlocality of Bohmian mechanics, where the velocity of one particle can depend on the position of a distant entangled particle. The results show that the trajectories of the first photon are indeed nonlocally influenced by an external control on the distant second photon, supporting the interpretation that the apparent inconsistencies arise from neglecting Bohmian mechanics'
This document provides an introduction to quantum mechanics and why it is necessary for describing molecular properties. It summarizes key experiments that classical mechanics could not explain, including electron diffraction showing wave-like behavior of electrons and discrete emission spectra of atoms indicating quantized energy levels. The document introduces the Bohr model of the hydrogen atom which explained emission spectra by proposing electrons orbit in discrete, quantized energy levels. While providing a better explanation than classical mechanics, the Bohr model and other early quantum theories were still incomplete. The Schrodinger equation was later developed as a more fundamental description of quantum systems, though it was not fully derived from first principles.
The SHOPS project implemented a 5-year program in Namibia from 2010-2015 with three main goals: 1) Support the creation of an enabling environment for public-private partnerships, 2) Strengthen the role of private health providers in male circumcision, and 3) Increase commercialization of NGOs. The program worked to develop a public-private partnership framework, mapped private health services, trained private providers in male circumcision, established networks of circumcision providers, and piloted NGO commercialization through corporate partnerships. Key lessons included the importance of collaboration between public and private sectors, the need for technical assistance to support NGO commercialization, and using existing systems and incentives to engage private providers in expanding health services
This document discusses the relationship between vibrational frequency and the force constant of a covalent bond. It states that for a diatomic molecule acting as a simple harmonic oscillator, the restoring force is proportional to displacement, as described by Hooke's Law. It then provides the equation relating vibrational frequency, force constant, and reduced mass. Several examples are given of calculating force constants from given vibrational frequencies and reduced masses. The document also notes that a higher force constant corresponds to a stronger covalent bond.
Quantum mechanics is the science of the very small that explains the behavior of matter and energy at the atomic and subatomic level. Some key aspects of quantum mechanics include wave-particle duality, Heisenberg's uncertainty principle, Schrodinger's wave equation, quantum superposition, quantum entanglement, and more. Many experiments such as the double slit experiment provide evidence of these quantum effects.
D:\Edit\Super\For Submission 20100306\12622 0 Merged 1267687011Qiang LI
This document discusses a proposed mechanism for electron pairing and superconductivity in ionic crystals. It analyzes a one-dimensional ion lattice chain model and establishes a mechanism for electron pairing driven by lattice vibration modes. The analysis is extended to 3D ionic crystals, focusing on donor-acceptor systems. Electron pairing occurs between energy levels matched to the maximum vibration frequency ωM. Introducing an acceptor band can stabilize electron pairs across the acceptor and full bands, with a binding energy estimated to be at least hωM/(4π).
(v3) Phonon as carrier of electromagnetic interaction between vibrating latti...Qiang LI
With emphasis on time-dependency of electron-lattice system, we suggest the fallacy of presumed quantization in the context of electron-lattice system and propose the definition of phonons as carriers of electromagnetic interaction between electrons and vibrating lattice. We have investigated behaviors of electron-lattice system relating to “measured” energy, identified non-stationary steady state of electrons engaging in “electron pairing by virtual stimulated transitions”, recognized some origins of binding energy of electron pairs in crystals, and explained the state of electrons under pairing. Moreover, we have recognized the behavior and role of threshold phonon, which exists in electron pairing and is released by the electron from excited state, and have recognized the redundancy of the threshold phonon when the electrons under pairing have entered non-stationary steady state. We have also studied the effect of the stability of lattice wave on the evolution of the function of transition probability and on the stability of phonon-mediated electron pairs, the competition among multiple pairings associated with one same ground state, and determination of presence/absence of superconductivity by such competition.
This document summarizes elementary particles in physics. It describes how particles are classified into leptons and hadrons. Leptons include electrons, muons, taus and their neutrinos. Hadrons include baryons like protons and neutrons, and mesons. Interactions are also classified, including the electromagnetic, weak, and strong interactions. The electromagnetic interaction between charged leptons and photons is described based on local gauge invariance, resulting in a theory of quantum electrodynamics that agrees well with experiments.
1. The document discusses the derivation of de Broglie's equation relating the wavelength of matter waves to the momentum of particles. It then derives different forms of de Broglie's wavelength equation using kinetic energy and potential energy.
2. It lists properties of matter waves including that lighter particles have greater wavelengths. It derives the Schrodinger time-independent and time-dependent wave equations.
3. It applies the time-independent equation to a particle in an infinite square well, finding the wavefunctions and energy levels based on boundary conditions and normalization.
Dielectric Dilemma 1901.10805 v2 feb 4 2019Bob Eisenberg
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the epolarization of the vacuumf ..0 .......... Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws reliably describe circuits that switch in nanoseconds.
This document analyzes the phenomenon of electrostatic attraction between particles from an energy perspective. It proposes that the potential energy between charges is infinite, and justifies this through several analyses. It uses concepts from magnetism, relativity, and Maxwell's equations to show that the magnetic force originating from electron spin is the source of the electrostatic force between charges. This explains the continuous attraction of particles despite vibration and over time. Previous works only considered the energy needed to separate particles, but not the infinite energy holding them together.
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
петр карпов и сергей мухин статья магнитные вихриeconadin
This document summarizes research on the dielectric susceptibility of magnetoelectric thin films containing magnetic vortex-antivortex dipole pairs. Key points:
1) A model is proposed where magnetic vortices in the thin film possess electric charges due to magnetoelectric coupling, forming electric dipoles with antivortices.
2) Below the Berezinskii-Kosterlitz-Thouless transition temperature, vortex-antivortex pairs dominate over individual vortices due to lower energy.
3) The contribution of these magnetic vortex-antivortex dipoles to the dielectric susceptibility of the material is calculated. It is shown that the susceptibility diverges as the temperature approaches the BKT
The document summarizes a study investigating the dielectric susceptibility of magnetoelectric thin films containing magnetic vortex-antivortex pairs. The study models the magnetic subsystem using the XY model and incorporates a magnetoelectric coupling term. Magnetic vortices acquire electric charges proportional to their topological charge. Vortex-antivortex pairs form electric dipoles that contribute to the dielectric susceptibility. In the approximation of non-interacting dipole pairs, the susceptibility diverges as temperature approaches the Berezinskii-Kosterlitz-Thouless transition temperature. At low temperatures, the susceptibility takes an exponential form reflecting the thermal activation of vortex pairs.
This document discusses microwave spectroscopy and its application to determining properties of gas phase molecules. It can be summarized as follows:
1) Microwave spectroscopy utilizes photons in the microwave range to cause rotational energy level transitions in gas molecules. It is applicable to molecules with a permanent dipole moment in the gas phase.
2) The rotational energy levels of diatomic molecules can be modeled using a rigid rotor approximation. This allows derivation of an expression for rotational energy levels in terms of the rotational constant B, which depends on the molecule's moment of inertia.
3) Measurement of transition frequencies between rotational energy levels allows determination of the rotational constant B. This can then be used to calculate bond distances in diatomic molecules.
This document provides a list and overview of various subatomic and composite particles categorized by type, including:
- Elementary particles like fermions (quarks and leptons) and bosons that mediate forces
- Hypothetical particles predicted by theories like supersymmetry
- Composite particles like hadrons (baryons like protons/neutrons and mesons) and atomic/molecular structures
It describes key properties and classifications of the different particles, such as their constituents, charges, and roles in the standard model of particle physics.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
1) The document derives both the Schrodinger quantum equation and Einstein's relativistic energy-momentum relation from Maxwell's electric wave equation.
2) It does so by considering particles as oscillators and using Planck's quantum hypothesis. The electric field intensity vector is replaced by the wave function.
3) Several steps and equations are shown to first derive the Schrodinger equation, and then the electric polarization and special relativity concepts are used to derive Einstein's energy-momentum relation.
1) Maxwell's equations describe electromagnetic waves propagating through space and time. For time-varying fields, the full set of Maxwell's equations must be used.
2) By assuming time-harmonic fields with a sinusoidal time variation, Maxwell's equations can be simplified to phasor forms containing only spatial derivatives.
3) The phasor forms of Maxwell's equations can be reduced to Helmholtz wave equations for the electric and magnetic fields. Plane wave solutions representing uniform electromagnetic waves propagating in a given direction can be derived from these equations.
Lasers have several key characteristics including monochromaticity, directionality, intensity, and coherence. They work by inducing stimulated emission of photons from atoms in an excited meta-stable state, achieving population inversion. This process is triggered by stimulated emission and results in an intense, highly directional beam of coherent, monochromatic light. Common lasers include ruby, helium-neon, and semiconductor diode lasers. Lasers have numerous applications due to their unique light properties.
Experimental nonlocal and surreal Bohmian trajectories.Fausto Intilla
The document summarizes an experiment that examines nonlocal and surreal Bohmian trajectories by entangling two photons and determining the trajectory of one photon using weak measurements and postselection. The experiment aims to validate the resolution proposed by Hiley et al. that the seemingly contradictory behavior of Bohmian trajectories predicted in the presence of a Welcher Weg measurement device is due to the manifest nonlocality of Bohmian mechanics, where the velocity of one particle can depend on the position of a distant entangled particle. The results show that the trajectories of the first photon are indeed nonlocally influenced by an external control on the distant second photon, supporting the interpretation that the apparent inconsistencies arise from neglecting Bohmian mechanics'
This document provides an introduction to quantum mechanics and why it is necessary for describing molecular properties. It summarizes key experiments that classical mechanics could not explain, including electron diffraction showing wave-like behavior of electrons and discrete emission spectra of atoms indicating quantized energy levels. The document introduces the Bohr model of the hydrogen atom which explained emission spectra by proposing electrons orbit in discrete, quantized energy levels. While providing a better explanation than classical mechanics, the Bohr model and other early quantum theories were still incomplete. The Schrodinger equation was later developed as a more fundamental description of quantum systems, though it was not fully derived from first principles.
The SHOPS project implemented a 5-year program in Namibia from 2010-2015 with three main goals: 1) Support the creation of an enabling environment for public-private partnerships, 2) Strengthen the role of private health providers in male circumcision, and 3) Increase commercialization of NGOs. The program worked to develop a public-private partnership framework, mapped private health services, trained private providers in male circumcision, established networks of circumcision providers, and piloted NGO commercialization through corporate partnerships. Key lessons included the importance of collaboration between public and private sectors, the need for technical assistance to support NGO commercialization, and using existing systems and incentives to engage private providers in expanding health services
Taylor Oliver brewed an American IPA called Rocket Man IPA. The lab report details the brewing process and calculations. A multi-step mash was performed to convert starches to fermentable sugars. Hops from three varieties were added at multiple times during the 90 minute boil to contribute bitterness and aromas. Yeast from another batch was pitched to begin fermentation. Calculations were shown to determine bitterness levels, alcohol content, and attenuation from the original and final gravities.
International Awards Multiple choice questions Vibhor Agarwal
This document provides information about various international awards winners from 2013-2014. It lists the winners of the Golden Globe award for best actor in 2014 (Matthew McConaughey), the Nobel prize for literature in 2014 (Patric Modiano), and the Grammy lifetime achievement award in 2013 (Late Pt. Ravi Shankar) among others. It also includes multiple choice questions about each award winner.
La receta describe cómo preparar un asado negro colombiano. Se marina la carne en vino tinto, ajo y especias antes de sellarla en aceite de maíz con papelón hasta que quede negra. Luego se agregan cebollas, tomates y agua para cocinar a fuego lento hasta que la carne esté tierna.
The document discusses the results of a study on the impact of COVID-19 lockdowns on air pollution. Researchers found that lockdowns led to significant short-term reductions in nitrogen dioxide and fine particulate matter pollution globally as transportation and industrial activities declined substantially. However, the document notes that continued long-term progress on air quality will require systemic changes rather than temporary reductions brought about by economic shutdowns.
En la actualidad los hospitales públicos son los responsables de brindar el servicio de urgencias, cuidados intensivos y cuidados intermedios a más del 55% de la población colombiana, estos servicios están regidos por atención 24/7 (Horas/Días) y debido a la demanda que presentan se requiere de atención y control permanente. El desarrollo de las TIC ha logrado mejorar estos servicios por medio de la implementación de sistemas de monitoreo que básicamente llevan a medio digital los parámetros vitales de una paciente y así el personal mantiene un contacto permanente sin necesidad de estar presencialmente con el paciente.
Es por esto que la problemática a estudiar es baja inversión y capacidad instalada de las TIC para servicios de III y IV nivel hospitalario.
La computadora es una máquina electrónica que puede recibir, procesar y devolver datos. Está compuesta de hardware (partes físicas como la CPU, memoria y gabinete) y software (programas y aplicaciones). Ha evolucionado a través de cinco generaciones desde las primeras computadoras de bulbos hasta las actuales de inteligencia artificial.
Labor Day is celebrated differently in Ecuador and Mexico. In Ecuador, Labor Day is on May 1st and commemorates the establishment of an eight hour workday and the martyrs of the Haymarket Riot in Chicago. It is a day of struggle and tribute for workers' rights. In Mexico, the constitution recognizes workers' rights, including an eight hour workday, one rest day per six work days, fair wages, and the right to form unions. On Labor Day in Mexico City, there are worker parades and protest marches organized by unions to voice complaints to authorities and advocate for workers.
This document summarizes the theoretical framework, instruments, and design of a study evaluating the effectiveness and cost-effectiveness of long-term psychoanalytic treatment. The study uses a multiple cohort design to follow patients in four cohorts representing different phases of treatment: before treatment, one year into treatment, at the end of treatment, and two years post-treatment. Outcome measures assess symptomatic functioning and structural change, using both theory-based and a-theoretical instruments. The study aims to expand the evidence base for psychoanalytic treatment given difficulties with randomized controlled trials for long-term interventions.
Determinants of Evaluation Supply at the US EPA: A Case Study of the RCRA Ha...Nick Hart, Ph.D.
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1. FINAL REPORT CHEM F266 Page of1 22
CHEM F266
STUDY ORIENTED PROJECT
IISEMESTER 2015-16
PROJECT TITLE : QUANTUM TUNNELING TO EXPLAIN
OLFACTION IN ANIMALS
SUPERVISING FACULTY: Dr. Shamik Chakraborty
SUBMITTED BY : Siddharth Shankar Tripathi
2014B2A3365P
2. FINAL REPORT CHEM F266 Page of2 22
ACKNOWLEDGEMENTS
This being my first major project I faced many challenges throughout the
project , ranging from deciding its scope , to accessing the material over the
web and otherwise but I would thus like to highly thank my mentor Dr.
Shamik Chakraborty who adequately helped me throughout the project and
was flexible enough to let me do anything wayward which was not in any
close connection with the project . He guided me very subtly and encour-
aged me towards the right direction for which I am grateful.
Also I would like to take the opportunity to thank the
head of the department , Dr. Anil Kumar for giving his due permission to let
me do this project .
3. FINAL REPORT CHEM F266 Page of3 22
ABSTRACT
The project involves the study of the process of olfaction in mammals. As was
suggested by Luca Turin in 1996 , the smelling systems of our body utilise the
process of tunneling in order to differentiate between different kinds of smell, but
in principle this theory has seen a lot of abnormalities which cannot be explained .
Thus at the moment , smell is a physical process used by us all, but fully under-
stood by none. The kind of electron tunneling has been speculated to be IETS
( inelastic electron tunnelling ).
In the project I have tried to understand the process of tunneling in
detail and using it as the base have carried its use to try to understand the
process of tunneling occurring in humans. After reaching to a comfortable enough
position I have then tried to investigate into the physiological details of the
process.
4. FINAL REPORT CHEM F266 Page of4 22
TUNNELING :
It is very rare or almost impossible for a classical particle to
pass through a wall or any physical barrier of such sort. This is fairly obvious as the par-
ticle size is a very big constraint that makes such a happening difficult task. But such a
process is performed by quantum particles very easily by a process known as quantum
tunnelling.
HOW DOES THIS WORK ?
Imagine that an electron, for example, is a marble sitting in one of two depressions sep-
arated by a small hill, which represent the effects of a sculpted electric field. To cross the
hill from one depression to the other, the marble needs to roll with enough energy. If it
has too little energy, then classical physics predicts it can never reach the top of the hill
and cross over it.
Tiny particles such as electrons, however, can still make it across even if
they don't have enough energy to climb the hill. Quantum physics describes such parti-
cles as extended waves of probability—and it turns out that there is a probability that
one of them will "tunnel" through the hill and suddenly materialise in the other depres-
sion, even though the electron can't occupy the high ground between the two low spots.
Figure 1. Depicting tunneling of wave through a barrier
Quantum tunnelling (or tunneling) refers to the quantum mechanical phe-
nomenon where a particle tunnels through a barrier which is classically forbidden. The
phenomenon of tunneling is an important consequence of quantum mechanics. Consid-
5. FINAL REPORT CHEM F266 Page of5 22
er a particle with energy E in the inner region of a one-dimensional potential well V(x). (A
potential well is a potential that has a lower value in a certain region of space than in the
neighbouring regions.) In classical mechanics, if E < V (the maximum height of the po-
tential barrier), the particle remains in the well forever; if E > V , the particle escapes. In
quantum mechanics, the situation is not so simple. The particle can escape even if its
energy E is below the height of the barrier V, although the probability of escape is small
unless E is close to V. In that case, the particle may tunnel through the potential barrier
and emerge with the same energy E.
THE BARRIERS IN THE PATH OF A WAVE ( ELECTRON MOVING AS A WAVE )
1) THE POTENTIAL STEP:
For a time independent potential, the wave function can be factorised as Ψ(x, t) = e−iEt/
ψ(x), where ψ(x) can be obtained from stationary form of the Schrodinger equation,
(time independent) .
Since here E and V(x) are assumed to be finite so must be the double de-
rivative of x . This condition forces the implication that : both ψ(x) and ∂xψ(x) must be
continuous functions of x, even if V has a discontinuity.
Figure 2 . This depicts the barrier extending from x=0 to x= infinity.
6. FINAL REPORT CHEM F266 Page of6 22
Assuming that a beam of particles withe kinetic energy E move from right to left are be-
ing incident at x=0 position of the barrier. Now if the beam has amplitude of one unit and
the reflected and transmitted wave are marked by r and t we have the wave functions
given by :
here the definitions of k should be taken note of . for x<0 k= (2mE/h2)1/2 and for x>0
k=(2mE/h2)1/2 .Now to make this system continuous at x=0 we obtain the relation 1+r=t
and ik<(1 − r) = ik>t leading to reflected and transmitted amplitudes ,
The reflectivity, R, and transmittivity, T, are defined by the ratios,R = reflected flux/inci-
dent flux , T = transmitted flux/incident flux .
Keeping the values for all kind of fluxes obtained , we solve for the solution and get
7. FINAL REPORT CHEM F266 Page of7 22
Figure 3. A graph depicting Reflectivity vs Transmittivity as the ratio of the energy of the wave
and the potential barrier values vary .
2) THE POTENTIAL BARRIER :
This is the most basic geometry of a scattering experiment to be discussed. In this phe-
nomenon a beam of particles is “deflected” by a local potential. Here the barrier is locat-
ed form x=0 to x=a , the wave function is of the form eik1x where k1= (2mE/h2)1/2 and
the wave functions only differ in their complex amplitudes after encountering the barrier
the transmitted wave function only goes in a change of amplitude and a phase shift. now
the relative phase changes can be parameterised as :
Applying the continuity conditions on the wave function, ψ, and its derivate , ∂xψ, at
the barrier interfaces at x = 0 and x = a, and then solving for four unknowns r , T , A and
B we get to the result :
8. FINAL REPORT CHEM F266 Page of8 22
which results into a transmittivity of
and the reflectivity , R=1-T . So, for barrier heights in the range E V0 0, the transmit-
tivity T shows an oscillatory behaviour with k2 reaching unity when k2a = nπ with n inte-
ger. When the energy of the incident particles falls below the energy of the barrier, 0 E
V0, a classical beam would be completely reflected. How- ever, in the quantum sys-
tem, particles are able to tunnel through the barrier region and escape leading to a non-
zero transmission coefficient. In this regime, k2 = iκ2 becomes pure imaginary leading to
an evanescent decay of the wave function under the barrier and a suppression, but not
extinction, of transmission probability.
Figure 4. Transmission probability of a finite potential barrier
9. FINAL REPORT CHEM F266 Page of9 22
Figure 5. Real part of the wave function for E/V0 = 0.6 (top), E/V0 = 1.6 (middle),
and E/V0 = 1 + π2/2 (bottom), where mV0a2/2 = 1. In the first case, the system shows tunneling
behaviour, while in the third case, k2a = π and the system shows resonant transmission. [Image
courtesy : advanced quantum chemistry ,chapter 3 of book published in
THE DIFFERENT THEORIES OF OLFACTION :
1) The lock and key model :
This was proposed by Axel and Buck . They proposed that the receptors belonged to the
class G of proteins (GPCRs) a type that will allow only specific odourants to bind to it on
the basis of their shape and size. Odourants and receptors can be tough to resemble as
a lock and key model . The theory was proposed with the view that like almost all other
systems of the body the process of olfaction wouldn't be much different and would cor-
respond to the same. The form of the pocket depends greatly on the sequence of amino
acids forming the protein and hence the corresponding three dimensional structure.
Thus, the sequence of amino acids that make the protein is crucial. A single change in
the order can change the shape of the pocket leading to changes in the chemicals that
fit into the pocket. A sequence of chemical events is initiated within a cell that involve
molecules called second messengers by the conformational changes in receptor pro-
10. FINAL REPORT CHEM F266 Page of10 22
teins caused by their binding with a fitting chemical (ligand). The degree to which a large
number of ion channels are opened is affected by a single odour molecule through the
second-messenger signals produced when they bind to a receptor protein. Large
enough potentials are produced by these actions.
CHALLENGES TO THE MODEL :
A lot of structured molecules have been discovered where differently structured
odourants create same olfaction senses while similar structured odourants have created
different olfaction senses.
Figure 6. Depicts the anomaly between shape similarity and smell [Image courtesy Google]
For example :
Hydrogen Sulphide and Decaborane are different in structure but smell very similar , in
the same manner ferrocene and nickelocene are similar in structure but smell complete-
ly differently .
THE ALTERNATE SWIPE CARD MODEL :
This is the alternate model as developed by Turin to explain the the anomalies in the
lock and key model.
The model speculates that shape is important for the odourant molecule to dock but
other specifications are also of utmost importance for olfaction. For e.g. a lot of credit
cards might fit into an ATM machine but only with an appropriate pin number can they be
used to withdraw cash from the machine.
The additional essential information that we use in our model is molecular vibrational
frequency of the odourant molecule.
The Turin model (our main discussion topic) proposes that electron transfer through the
11. FINAL REPORT CHEM F266 Page of11 22
odourant preferentially occurs on when the molecule has the right vibrational frequency.
The model places the use of INELASTIC ELECTRON TUNNELING which we shall talk
about now in the further discussion :
IETS is a non optical form of vibrational spectroscopy relying on the interaction between
electrons tunneling across a narrow gap between metallic electrodes and molecule in
the gap.
Inelastic tunneling describes tunneling between two states with different
energies . In order for energy to be conserved , something else has to pick up some en-
ergy from or deposit it with the electron. The typical energy source/sink is the crystal lat-
tice of the material , whose vibrations are called sound or , in quantum language ,
phonons.
a) shows energy band diagrams for tunneling while b) shows corresponding I vs V dia-
gram.
Figure 7. Depicts IETS model as used in inorganic systems
Turin's model almost like all normal tunneling models uses two
points of contact between the odourant and the receptor i.e. namely the donor (D) and
the acceptor energy level (A).
The favourable condition for the inelastic tunneling to occur is that the electronic differ-
ence between D and A sites must match the vibrational energy taken up by odourant
(M).
12. FINAL REPORT CHEM F266 Page of12 22
Figure 8. This is the kind of tunneling desired by us under the circumstances as stated in
the model.
Figure 9. Another type of electron tunneling which can happen but not useful to the model that
we use.
THE DIFFERENT ROUTES TAKEN BY THE ELECTRON IN THE
COURSE OF TUNNELING
13. FINAL REPORT CHEM F266 Page of13 22
So far, we have established that as an electron transfers from D to A, it alters forces on
M, so causing a change in the odourant’s vibrational state. This behaviour has parallels
in a lot of other solid state systems. Until we have more information about the receptor
structure, doubts must remain as to precisely which groups D and A correspond. We
have assumed that D and A are relatively localised, and that the odourant molecule M in
the receptor is close to either D or A or it is perhaps equidistant and equally localised be-
tween them. The donor and acceptor species will have discrete energies, unlike the
electrodes in most inorganic inelastic tunnelling experiments.
This would be realistic if we believe the likelihood that these electron
source/sinks are amino acids and if we compare to distances between important
residues for rhodopsin. Site-directed mutagenesis studies have determined that for
odourant recognition in MOR-EG (mouse olfactory receptor) there are nine amino acids
involved directly at the binding site, with Ser113 (amino acid) being a crucial H-bond
donor for odourants with aliphatic alcohols. It is noteworthy that none of the nine is
strongly conserved and indeed some are at sites that are highly variable. Thus they can
only be associated with binding or modifying the donor and acceptor characteristics.
Figure 10. A configuration coordinate diagram to show the initial state (the left curve) and the
final state (the right curves) where there are two options : the inelastic (n=1) versus the elastic
(n=0) route. [Image courtesy : google images]
Two different kinds of routes have been proposed to be taken by an electron during the
tunneling process in the receptor protein.
14. FINAL REPORT CHEM F266 Page of14 22
Figure 11. A scheme for the proposal of electron transfer in the olfactory receptor
with intra-protein electron transfer. Only 5 transmembrane helices for the olfactory receptor are shown
(cylinders) here for clarity. (a) The odourant approaches the receptor, meanwhile an electron is present at
donor site D; (b) The odourant docks at the ligand binding domain, the overall configuration of receptor
and odourant changes (c) The electron jumps from D to A, causing the odourant to vibrate (d) The
odourant is expelled from the ligand binding domain.
Figure 12. A scheme for the proposal of electron transfer in the olfactory receptor. Only
5 transmembrane helices (of the 7 in total) for the olfactory receptor are shown (cylinders) here for clarity.
(a) The odourant approaches the receptor, meanwhile an electron moves to position RD on a helix; (b)
The odourant docks at the ligand binding domain, the overall configuration of receptor and odourant
changes, meanwhile the electron tunnels within the protein to D and it spends some time there; (c) The
electron jumps from D to A causing the odourant to vibrate; (d) The odourant is expelled from the ligand
binding domain and the electron tunnels within the protein to site RA. Signal transduction is initiated with
the G-protein release. [ Image courtesy : Sensors 2012, 12, 15709-15749 ] .
15. FINAL REPORT CHEM F266 Page of15 22
DEVELOPMENT OF THE HAMILTONIAN FOR THE MODEL :
Electron transfer between the donor and acceptor can be described through or modelled
by the hamiltonian :
this accounts for the essential physical interactions in the system . Here HR denotes the
olfactory receptor hamiltonian , HR-O describes the coupling interaction between the ol-
factory receptor and an odourant molecule, HR-env and HT accounts for electron tunneling
from donor to acceptor sites of the olfactory receptor.
Thus the hamiltonian describes each and every interaction of the components in olfac-
tion.
Simple Huang–Rhys Factor Model :
• QUESTION — WHAT IS THIS MODEL ?
• ANSWER — The Huang-rhys factor gives a measure of the coupling of the olfactants
to the rapid movement of the electronic charge from the donor D to the acceptor A.
The model may be applied to any one of the ways in which the electron charge is sup-
posed to tunnel through D to A whose sudden energy change (force change on the
odourant molecule because of the electron tunneling through it in principal) causes M to
change vibrational states.
Huang-rhys factor comes out to be S = E2q2/(2Mh︎ω3) .
The energy of Donor and Acceptor energy levels is then calculated and also needs to be
decided what effective mass M and charge q should be taken.
Now when the electron passed from donor to acceptor change in force =
16. FINAL REPORT CHEM F266 Page of16 22
The Huang–Rhys factors can be calculated using a full electronic struc-
ture code. This is normally done by combining total energies from four calculations;
namely, for the system relaxed for the charge at R
⃗
D , calculate the energies when the
electron is on D and when it is on A, and correspondingly, for the system relaxed for the
charge at R
⃗
A, calculate the energies when the electron is on D and when it is on A.
There is some redundancy in these calculations, but this compensates somewhat for
working close to the limits of accuracy of electronic structure codes.
MATRIX ELEMENTS IN CALCULATION OF THE FACTOR :
The important electronic states are those where the electron is on the donor, represent-
ed by the notation |D⟩, and when the electron is on the acceptor, this is represented by
the notation |A⟩. Here making the assumption that the electronic wave functions evolve
adiabatically, as electron motion is very rapid compared with the nuclear motion during
transitions. The Hamiltonian to describe these energetic states is:
where t is very small (we get T1=87 ns , the time taken in the movement of electron
when odourant is absent and ︎ T2=1:3 ns, the time taken by the electron when it tunnels
through the odourant ; which satisfies the condition ︎ T2T1 , and shows that the overall
time for odour recognition is not limited by the discrimination process) the donor and ac-
ceptor are weakly coupled. Introducing an odourant M into the equation then the elec-
tron can go from D to A via the molecule (or via a different route) with state |M⟩. The
Hamiltonian for this scenario is:
17. FINAL REPORT CHEM F266 Page of17 22
In order to generalise to an effective two state Hamiltonian, the following determinant
was produced :
Making the secular equations and solving of the coefficients we finally derive the time
period of tunneling in the process which come out to be after calculation as
Approximating ε = εD as , it is not known whether the energy eigenstate ε, but the as-
suming ε = εD or εA, since εD and εA differ very little (meV), as compared with the dif-
ference between εD and εM (10’s eV). Thus the initial electronic state will involve an
admixture of D and M due to the presence of the odourant, and the final electronic state
is similarly an admixture of A and M. This implies the presence of an odourant M is inte-
gral to an electron transfer process.
Figure 13. A table depicting time scales of different processes in different processes. [Table cour-
tesy Sensors 2012, 12, 15709-15749]
18. FINAL REPORT CHEM F266 Page of18 22
DISCUSSION OF THE DONOR AND ACCEPTOR SPECIFICA-
TIONS :
For an inelastic tunnelling mechanism (IETs) to work,
the molecular units D and A have to satisfy certain well defined conditions. Just what D
and A are is not at the moment clear. They have been speculated to be common units
among the likely receptor structures. They must be able to occur in two charge states,
which can be assumed as full and empty (so the transition results from D(full)A(empty)
to D(empty)A(full) { here full is the situation when electron is in the particular energy
state } ), though that is possible for many possible molecular units. Transition metals, of-
ten found in living systems, are among the species that can occur in several charge
states. The D and A units should have the capability to be able to revert back to their
original states many times, i.e., D and A should not be destroyed in the one cycle of ol-
faction process. It must be possible to feed an electron into D and remove an electron
from A (inter- chain model) or return the electron to D (intra-chain model). To detect
odourants within milliseconds, through tunneling via an odourant can be much faster, the
replenishment of D and A should be within ms but not longer.
Whilst that is not a strong constraint as regards timescale, it
does require other reactions outside the receptor to maintain electrochemical equilibria
that drive these motions. It is to be noted also , that D and A must be sharp energy lev-
els, which means only weak interactions to cause broadening. This is consistent with the
calculated results, where all relevant interactions appear weak. The most important re-
strictions on D and A (energy levels ) is the need for a small energy splitting εD − εA that
is almost equal to the small (but in principal approximate) vibrational quantum ︎ω0. Most
olfactants M and many possible molecular units of the receptor are closed shell systems,
and in which the gap between the highest occupied molecular orbital (HOMO) and low-
est unoccupied molecular orbital (LUMO) levels is two orders of magnitude too large.
Electron transfer from the HOMO of one unit to the LUMO of another is ruled out by their
large energy difference, perhaps even 10 eV.
19. FINAL REPORT CHEM F266 Page of19 22
A PHYSIOLOGICAL DISCUSSION :
Journey of the odourant to the receptor :
The odorant’s journey begins as sniffed through the nose and meets the olfactory ep-
ithelium at the top of the nasal cavity. At the epithelium it meets the cilia which extend
from the neuron’s main body into the mucus layer. At this interface between mucus and
inside the cell, the odorant meets the olfactory receptor. Whatever happens at this point
to produce a discriminant signal results in ionic cascades that depolarise the cell.
Figure 14. The figure depicts diagrammatically what happens when we inhale a possible odourant
molecule. [Image courtesy : Anal Bioanal Chem (2003) 377 : 427–433 ]
The olfactory receptors definition has been one of the most tricky part of the physiologi-
cal understanding of the process. It has been proved by Axel and Buck to be GPCR
class of proteins for which discovery they received the nobel prize in 2004. This GPCRs
model has been proposed by Breer . The N-terminal extend into the extracellular layer,
the C-terminaI extend into the olfactory sensory neuron (OSN). The seven trans mem-
brane helices are represented here as cylinders connected by flexible loops. They are
surrounded by lipids, the hydrophobic tails forming a barrel around the receptor, within
the barrel the odourant binds, the polar heads point towards the ‘wet’ layers.
20. FINAL REPORT CHEM F266 Page of20 22
Figure 15. The model showing the representation of the GPCR as perceived by Breer. [image
courtesy : Anal Bioanal Chem (2003) 377 : 427–433 ]
These proteins work via release of a G-protein into the cytoplasm which causes sec-
ondary messengers initiates a signalling process.
21. FINAL REPORT CHEM F266 Page of21 22
CONCLUSION
The process of smell is still one of the most ambiguous process that has yet not been
completely described by scientists. As we see in the report , the Donor levels , Acceptor
levels , path of the electrons tunneling before and after the process , any extra energy
produced or used by the process is not entirely defined. The lock and key theory fails
several tests and the swipe card model provides an alternate which solves many issues.
Despite being a viable alternate it leaves many questions unanswered
and many solutions undelivered on many fronts which have a lot of scope to be investi-
gated in. We also see that how , just by a change of coordination factor a lot of things
might change and how even for the new theory the basic requirements for the body to
recognise odour ( shape , size of pocket etc) remain the same. The biggest question
which still remains is that is really vibrational theory a solution out of the crisis ?
22. FINAL REPORT CHEM F266 Page of22 22
BIBLIOGRAPHY
1. Jennifer C. Brookes (2011) : Olfaction: the physics of how smell works?, Contempo-
rary Physics, 52:5, 385-402
2. Review The Swipe Card Model of Odourant Recognition , Jennifer C. Brookes , An-
drew P. Horsfield and A. Marshall Stoneham Sensors 2012, 12, 15709-15749;
3. Could Humans Recognize Odor by Phonon Assisted Tunneling?( Jennifer C. Brookes,
Filio Hartoutsiou, A. P. Horsfield, and A. M. Stonehamx , PRL 98, 038101 (2007))
4. Manuel Zarzo ,The sense of smell: molecular basis of odorant recognition , Biol. Rev.
(2007), 82, pp. 455–479.
5. Phys. Chem. Chem. Phys., 2012, 14, 13861–13871